2008ApJ...686..603J

We explore the possibility that the observed eccentricity distribution of extrasolar planets arose through planet-planet interactions, after the initial stage of planet formation was complete. Our results are based on ∼3250 numerical integrations of ensembles of randomly constructed planetary systems, each lasting 100 Myr. We find that for a remarkably wide range of initial conditions the eccentricity distributions of dynamically active planetary systems relax toward a common final equilibrium distribution, well described by the fitting formula dn∝eexp[-(1)/(2)(e/0.3)²]de. This distribution agrees well with the observed eccentricity distribution for e≳0.2 but predicts too few planets at lower eccentricities, even when we exclude planets subject to tidal circularization. These findings suggest that a period of large-scale dynamical instability has occurred in a significant fraction of newly formed planetary systems, lasting 1-2 orders of magnitude longer than the ∼1 Myr interval in which gas giant planets are assembled. This mechanism predicts no (or weak) correlations between semimajor axis, eccentricity, inclination, and mass in dynamically relaxed planetary systems. An additional observational consequence of dynamical relaxation is a significant population of planets (≳10%) that are highly inclined (≳25°) with respect to the initial symmetry plane of the protoplanetary disk; this population may be detectable in transiting planets through the Rossiter-McLaughlin effect.